{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "cWmjVDJ16wRK"
   },
   "source": [
    "# CS490/590 Tutorial 2: Multi-Class Classification with PyTorch\n",
    "\n",
    "In this tutorial, we'll go through an example of a multi-class\n",
    "linear classification problem using PyTorch.\n",
    "\n",
    "However, PyTorch hides a lot of details of the computation,\n",
    "both of the computation of the prediction, and the computation of the gradients. In your later\n",
    "projects, you'll work with both numpy to understand deeply how your models actually work, but\n",
    "also learn PyTorch to gain practical skills in building machine learning models.\n",
    "\n",
    "In the process, we will:\n",
    "\n",
    "- Introduce the MNIST dataset, which contains 28x28 pixel images of hand-written digits\n",
    "- Introduce how to use of PyTorch to build and train models\n",
    "- (If we have time) explore the effect of certain settings on our model:\n",
    "    - Data set size\n",
    "    - Batch size\n",
    "    - Regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "rlfGgFvr6wRQ"
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3vgq7k7O6wRR"
   },
   "source": [
    "## Data\n",
    "\n",
    "The MNIST dataset contains black and white, hand-written (numerical) digits\n",
    "that are 28x28 pixels large. This is a data set that is typically used for\n",
    "demonstrations of machine learning models, and as a first data set to test\n",
    "new types of models.\n",
    "\n",
    "We will download the dataset. For simplicity, we'll only use the first 2500\n",
    "images in the MNIST dataset. The first time you run this code, we will download\n",
    "the MNIST dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "nbT6XDE06wRR",
    "outputId": "8c20932f-3da1-4314-b743-94b43cdaa2d8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading https://www.itl.nist.gov/iaui/vip/cs_links/EMNIST/gzip.zip to data/EMNIST/raw/gzip.zip\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "045209593a4a46939b4df632b2a5a47e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/561753746 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting data/EMNIST/raw/gzip.zip to data/EMNIST/raw\n",
      "(<PIL.Image.Image image mode=L size=28x28 at 0x7F9C7FBB4D90>, 4)\n"
     ]
    }
   ],
   "source": [
    "from torchvision import datasets\n",
    "#from torchvision import datasets.MNIST\n",
    "\n",
    "# load the training data\n",
    "mnist_train = datasets.EMNIST('data', train=True, split='mnist', download=True)\n",
    "mnist_train = list(mnist_train)[:2500]\n",
    "\n",
    "print(mnist_train[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7J0qtRfa6wRR"
   },
   "source": [
    "Let's take a look at some of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 252
    },
    "id": "OeGZWFRh6wRR",
    "outputId": "f95297e5-4db4-44ad-e05a-205e4075823f"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the first 18 images in the training data\n",
    "import matplotlib.pyplot as plt\n",
    "for k, (image, label) in enumerate(mnist_train[:18]):\n",
    "    plt.subplot(3, 6, k+1)\n",
    "    plt.imshow(image, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6ozodu6z6wRS"
   },
   "source": [
    "PyTorch has code written for us to convert an image into numerical pixel features.\n",
    "The tensor still preserves the 2D geometry of the image (we still get a `1x28x28` shape) \n",
    "and does not yet flatten the image into a vector (to get a `1x784` shape) like we discussed\n",
    "in lecture."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "SpJcr8Hj6wRS",
    "outputId": "83deb0c5-9cd8-4d68-b4db-9d7bfb2673b4"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from torchvision import transforms\n",
    "# transform the image data type to a 28x28 matrix of numbers\n",
    "img_to_tensor = transforms.ToTensor()\n",
    "\n",
    "# convert the last image we saw into a tensor\n",
    "img_tensor = img_to_tensor(image)\n",
    "img_tensor.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OMPh28Go6wRS"
   },
   "source": [
    "If we want to convert the entire dataset into these tensor representations (as opposed to\n",
    "PIL.Image objects), there is a `transform` parameter that we can use when loading the MNIST\n",
    "dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UeKEFQzb6wRS",
    "outputId": "092271ce-7ee6-46fb-b1c4-59a5a071d736"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(tensor([[[0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0275, 0.1451, 0.1451, 0.0706, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0863, 0.3725, 0.8431, 0.8510, 0.4784, 0.0471, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0078, 0.0431, 0.3569,\n",
      "          0.9098, 0.9843, 0.9961, 0.9961, 0.9686, 0.7451, 0.0157, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0078, 0.0824, 0.1529, 0.3216, 0.5529, 0.8667,\n",
      "          0.9961, 0.9961, 0.9961, 0.9961, 0.9961, 0.8706, 0.0353, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.2549, 0.6667, 0.8510, 0.9137, 0.9804, 0.9961,\n",
      "          0.9961, 0.9843, 0.8902, 0.9765, 0.9961, 0.9608, 0.1333, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.2980, 0.8078, 0.9843, 0.9961, 0.9961, 0.9647,\n",
      "          0.7922, 0.3725, 0.1804, 0.8510, 1.0000, 0.9922, 0.4000, 0.0118,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0275, 0.1804, 0.6667, 0.8431, 0.7961, 0.4980,\n",
      "          0.1333, 0.0275, 0.1294, 0.8039, 0.9961, 0.9922, 0.3725, 0.0118,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0078, 0.0157,\n",
      "          0.0157, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0078, 0.0157, 0.0157, 0.0000,\n",
      "          0.0000, 0.0000, 0.0667, 0.6353, 0.9961, 0.9961, 0.4510, 0.0157,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0353, 0.1804, 0.6667, 0.8431,\n",
      "          0.7961, 0.4745, 0.0078, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0824, 0.6784, 0.9961, 0.9882, 0.3216, 0.0078,\n",
      "          0.0000, 0.0000, 0.0039, 0.1294, 0.5451, 0.8157, 0.9843, 0.9961,\n",
      "          0.9922, 0.8353, 0.0157, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.1529, 0.8510, 0.9961, 0.9137, 0.0863, 0.0000,\n",
      "          0.0157, 0.1333, 0.5451, 0.8667, 0.9961, 0.9961, 0.9961, 0.9961,\n",
      "          0.9804, 0.7882, 0.0157, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.3216, 0.9137, 0.9961, 0.8275, 0.1608, 0.1529,\n",
      "          0.4510, 0.6941, 0.9804, 0.9961, 1.0000, 0.9961, 0.9686, 0.8627,\n",
      "          0.5451, 0.3020, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0039, 0.5059, 0.9647, 0.9961, 0.9490, 0.9765, 0.9804,\n",
      "          0.9961, 0.9961, 0.9961, 0.9843, 0.8706, 0.8431, 0.3569, 0.0431,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0157,\n",
      "          0.0196, 0.1412, 0.7412, 0.9490, 0.9961, 0.9961, 0.9961, 0.9961,\n",
      "          0.9961, 0.9804, 0.9098, 0.6706, 0.2000, 0.1451, 0.0275, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0314, 0.1333, 0.4980, 0.7961,\n",
      "          0.8510, 0.9176, 0.9961, 0.9961, 0.9961, 0.9961, 0.9804, 0.9608,\n",
      "          0.6235, 0.2039, 0.0824, 0.0118, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0314, 0.4941, 0.8000, 0.9647, 0.9961,\n",
      "          0.9961, 0.9961, 0.9961, 0.9961, 0.9647, 0.8157, 0.5059, 0.4471,\n",
      "          0.0863, 0.0039, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0392, 0.4980, 0.9922, 0.9961, 0.9961, 0.9961,\n",
      "          0.9608, 0.8627, 0.5490, 0.4902, 0.1804, 0.0314, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.3569, 0.8667, 0.9961, 0.9961, 0.9176, 0.8000,\n",
      "          0.4510, 0.1961, 0.0353, 0.0157, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0118, 0.7843, 0.9922, 0.9843, 0.9098, 0.3725, 0.1333,\n",
      "          0.0157, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.3529, 0.7843, 0.3725, 0.0863, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0275, 0.1255, 0.0275, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000],\n",
      "         [0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,\n",
      "          0.0000, 0.0000, 0.0000, 0.0000]]]), 4)\n"
     ]
    }
   ],
   "source": [
    "mnist_train = datasets.EMNIST('data', train=True, split='mnist', transform=img_to_tensor)\n",
    "mnist_train = list(mnist_train)[:2500]\n",
    "print(mnist_train[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yQqRodte6wRT"
   },
   "source": [
    "Now, we'll split this data into training and validation, and start to build our model.\n",
    "We won't need a test set for this tutorial, but in general we will also have a test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "GypSVQGG6wRT"
   },
   "outputs": [],
   "source": [
    "mnist_train, mnist_val = mnist_train[:2000], mnist_train[2000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "E1zYnK1U6wRT"
   },
   "source": [
    "## Linear Model in PyTorch\n",
    "\n",
    "To build a linear model in PyTorch, we create an instance of the class `nn.Linear`,\n",
    "and specify the number of input features, and the number of output features. For linear regression\n",
    "and binary classification, the number of output features is 1. For multi-class classification,\n",
    "we have as many outputs as there are classes.\n",
    "\n",
    "When using this model for classification, we'll need to apply the sigmoid or softmax\n",
    "activiation *afterwards*. That is, this object is only meant to handle the linear part of the\n",
    "model computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "VK4eCdX-6wRT"
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "\n",
    "example_model = nn.Linear(50, 1) # assume 50 features, 1 linear output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_uXAl_jN6wRT"
   },
   "source": [
    "The `example_model` object contains weights and biases of the model. By default, PyTorch\n",
    "initializes these values to a random number close to 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "l7qJYUBx6wRU",
    "outputId": "7ac4fe0b-b748-4330-8959-9b7e30d13936"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-4.3303e-02, -1.3204e-01,  1.8963e-03,  1.1912e-01,  9.0956e-02,\n",
      "          4.9142e-02,  2.0999e-02,  1.1877e-01,  4.4658e-02,  6.9490e-02,\n",
      "         -8.0287e-02, -1.3248e-01, -2.5683e-02,  4.5094e-02,  1.3373e-01,\n",
      "          1.4022e-01, -6.1331e-03, -5.1411e-02, -1.3955e-01,  1.2187e-01,\n",
      "          9.8455e-02,  7.9199e-02,  7.7525e-02, -6.0096e-02, -1.0018e-01,\n",
      "         -1.0082e-02, -1.1552e-01, -5.6761e-02,  8.1122e-03,  4.9194e-02,\n",
      "         -2.1610e-02,  1.2479e-01, -1.2426e-01, -6.4057e-02,  1.2356e-01,\n",
      "         -3.4235e-02, -5.6032e-02,  7.2563e-02, -5.3539e-02, -8.7507e-02,\n",
      "         -2.4357e-02, -1.0103e-04, -4.0625e-02, -5.4343e-02, -1.0633e-01,\n",
      "          1.1787e-01, -2.1330e-02,  4.2642e-02,  3.6839e-02, -1.4934e-02]],\n",
      "       requires_grad=True)\n",
      "torch.Size([1, 50])\n",
      "Parameter containing:\n",
      "tensor([-0.1364], requires_grad=True)\n",
      "torch.Size([1])\n"
     ]
    }
   ],
   "source": [
    "weight, bias = list(example_model.parameters())\n",
    "print(weight)\n",
    "print(weight.shape)\n",
    "print(bias)\n",
    "print(bias.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hI2H_jfO6wRU"
   },
   "source": [
    "If we create a new model, those initial parameters will change:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XQf71en86wRU",
    "outputId": "eda2679d-fb88-4645-c54f-0768bbb5b7c7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter containing:\n",
      "tensor([[-0.1275, -0.0048,  0.0426, -0.0963, -0.1267,  0.0101,  0.1400, -0.0448,\n",
      "         -0.1249,  0.0602,  0.0779,  0.0286,  0.0750, -0.1221, -0.0895, -0.0705,\n",
      "         -0.1273, -0.1041,  0.0331, -0.0717, -0.0636, -0.0745, -0.1171,  0.0204,\n",
      "         -0.1015,  0.0266, -0.0875,  0.0292,  0.0950, -0.0367, -0.1300, -0.0741,\n",
      "          0.0390,  0.0847,  0.1227,  0.0249, -0.1190, -0.0833,  0.0095,  0.0743,\n",
      "          0.0380, -0.1133,  0.1198, -0.1124, -0.1198, -0.1064, -0.0505, -0.0934,\n",
      "         -0.0558,  0.1274]], requires_grad=True)\n",
      "torch.Size([1, 50])\n",
      "Parameter containing:\n",
      "tensor([0.1044], requires_grad=True)\n",
      "torch.Size([1])\n"
     ]
    }
   ],
   "source": [
    "example_model = nn.Linear(50, 1)\n",
    "weight, bias = list(example_model.parameters())\n",
    "\n",
    "# These values should be different from above\n",
    "print(weight)\n",
    "print(weight.shape)\n",
    "print(bias)\n",
    "print(bias.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9LEHd0Xn6wRU"
   },
   "source": [
    "Now, let's create the actual model that we will train to solve the MNIST\n",
    "digit classification problem. How many input features do we have? How many\n",
    "output features do we need?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Eck1bIQW6wRU",
    "outputId": "b34db449-790e-43c2-f555-71d6a75ae3a1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([10, 784])\n",
      "torch.Size([10])\n"
     ]
    }
   ],
   "source": [
    "model = nn.Linear(784, 10) # 784 = 28*28\n",
    "\n",
    "# Let's verify that the shapes of the weights and biases are what we expect\n",
    "weight, bias = list(model.parameters())\n",
    "print(weight.shape)\n",
    "print(bias.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Uajt6sbx6wRU"
   },
   "source": [
    "## Making Predictions\n",
    "\n",
    "Let's see how we can make a prediction with this model. (You might find it strange that \n",
    "we're talking about how to make predictions *before* talking about how to train the model.\n",
    "The reason is that we will always train the model using a varient of gradient descent.\n",
    "So you can imagine that the weights of this model will eventually become more meaningful\n",
    "than it is now)\n",
    "\n",
    "We'll start with the simpler `example_model` first. The way that we make predictions\n",
    "is by starting with an input $x$ that has the required shape. Since `example_model` is\n",
    "just an example, we'll create a tensor with the appropriate shape, filled with random values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "yUC1KhnM6wRV",
    "outputId": "e2195c1f-4308-4a5b-ddbb-d4fb3ffb4110"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([50])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = torch.randn(50) # create a rank 1 tensor (vector) with 50 features\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EAcYMUgG6wRV"
   },
   "source": [
    "To make predictions, we apply the `example_model` as if it is a function, with the \n",
    "inputs as an argument:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DD21oTAo6wRV",
    "outputId": "3b007539-5264-44e2-85c8-9370c2adedf5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = example_model(x)\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EG6QE_W66wRV"
   },
   "source": [
    "If this model was used for binary classification, we might also need to apply the sigmoid \n",
    "function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VfGMgCQL6wRV",
    "outputId": "ae92b63a-21c4-492b-9056-979cc6a6cacf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.5221], grad_fn=<SigmoidBackward0>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.sigmoid(example_model(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bx_q-p8q6wRV"
   },
   "source": [
    "One nice thing about PyTorch is that it vectorizes and parallelizes the computation for us.\n",
    "So, if we had a *batch* of 32 inputs that we want to make predictions for, we can perform\n",
    "that computation using a single call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "69qdRsjm6wRW",
    "outputId": "4467ce45-e630-4b14-c7a7-0120688e3e41"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([32, 50])\n",
      "torch.Size([32, 1])\n"
     ]
    }
   ],
   "source": [
    "x = torch.randn([32, 50]) # a stack of 32 inputs\n",
    "print(x.shape)\n",
    "y = example_model(x)\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BieonEcN6wRW"
   },
   "source": [
    "(Note: The order of the dimensions in our input $x$ matters. The batch size always goes first,\n",
    "and the number of features always goes second)\n",
    "\n",
    "Now, let's try and make some \"predictions\" with our MNIST model!  We still have\n",
    "the variable `image_tensor` from earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "YvMENvtf6wRW",
    "outputId": "4b983284-1e29-467f-884c-dcae5349abe6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 28, 28])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img_tensor.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Td_PPwZ26wRW"
   },
   "source": [
    "However, the shape of this tensor is not what we need it to be.\n",
    "We need to *flatten* the image into either a rank 1 tensor (with shape [784])\n",
    "or a rank 2 tensor (with shape [1, 784]). We'll choose the latter, so\n",
    "that the transition to passing multiple images at the same time is easier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "rYBnqSJm6wRX",
    "outputId": "ee6cfc0d-bb69-4a96-ff8e-56492ae52d76"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1, 784])\n",
      "tensor([[-0.0077, -0.3822, -0.1441,  0.3224,  0.1157, -0.4486,  0.3002,  0.1210,\n",
      "          0.0326,  0.0066]], grad_fn=<AddmmBackward0>)\n",
      "torch.Size([1, 10])\n",
      "tensor([[0.0973, 0.0669, 0.0849, 0.1353, 0.1101, 0.0626, 0.1324, 0.1106, 0.1013,\n",
      "         0.0987]], grad_fn=<SoftmaxBackward0>)\n"
     ]
    }
   ],
   "source": [
    "x = img_tensor.view(1, 784)\n",
    "print(x.shape)\n",
    "z = model(x)\n",
    "print(z)\n",
    "print(z.shape)\n",
    "y = torch.softmax(z, dim=1)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rbGpudYI6wRX"
   },
   "source": [
    "The `dim=1` in the softmax tells PyTorch which dimension represents different\n",
    "images, and which one represents the different class labels. We want our\n",
    "outputs $y$ to be a probability distribution across the *classes*, and not\n",
    "the different images.\n",
    "\n",
    "## Loss Function\n",
    "\n",
    "In order for the network to be useful, we need to actually train it, so\n",
    "that the weights are actually meaningful, non-random values. As we mentioned\n",
    "before, we'll use the network to make predictions, then compare the predictions\n",
    "agains the ground truth via the loss function.\n",
    "\n",
    "PyTorch has standard loss functions that we can use: for example,\n",
    "`nn.BCEWithLogitsLoss()` for a binary-classification problem, and a \n",
    "`nn.CrossEntropyLoss()` for a multi-class classification problem like ours."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "id": "OU7zwzqy6wRX"
   },
   "outputs": [],
   "source": [
    "criterion = nn.CrossEntropyLoss()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Rje0uNem6wRX"
   },
   "source": [
    "This criterion can also be called as a function. It takes the logit prediction and\n",
    "ground-truth as parameters, and returns the loss. Two things to keep in mind\n",
    "for this function:\n",
    "\n",
    "1. Loss functions like this usually takes the **logit** as parameter, rather than\n",
    "   the post-softmax probability distributions. This is for numerical stability.\n",
    "2. This loss function also takes the ground-truth integer **index** as a parameter,\n",
    "   rather than a one-hot vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Rs_beoYO6wRX",
    "outputId": "c4576c9a-b051-4237-dc76-07404701fea5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(2.3016, grad_fn=<NllLossBackward0>)\n"
     ]
    }
   ],
   "source": [
    "loss = criterion(y, torch.Tensor([8]).long()) # digit 8 = the 8-th class\n",
    "print(loss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SWT2Bk_e6wRX"
   },
   "source": [
    "## Optimization and Weight Decay\n",
    "\n",
    "PyTorch also computes derivatives for us using *automatic differentiation*, which\n",
    "we (might) talk about in this course. In short, we can specify an **optimizer**\n",
    "(like Stochastic Gradient Descent), and use the optimizer to determine how to\n",
    "update the weights."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "id": "cm6pxibN6wRX"
   },
   "outputs": [],
   "source": [
    "import torch.optim as optim\n",
    "optimizer = optim.SGD(model.parameters(), lr=0.005) # lr = learning rate\n",
    "\n",
    "# There are three lines of code required to perform \n",
    "# a gradient descent update:\n",
    "loss.backward()       # compute updates for each parameter\n",
    "optimizer.step()      # make the updates for each parameter\n",
    "optimizer.zero_grad() # a clean up step for PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tQ9DNDHf6wRY"
   },
   "source": [
    "We can also use weight decay (L2 regularization) in PyTorch through the optimizer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "MxzFSkMQ6wRY"
   },
   "outputs": [],
   "source": [
    "optimizer = optim.SGD(model.parameters(), lr=0.005, weight_decay=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NdR0RAyh6wRY"
   },
   "source": [
    "## Batching\n",
    "\n",
    "PyTorch data loader also does batching for us!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zkcoQzgX6wRY",
    "outputId": "f464d2d5-553a-4f8c-ad02-684be8798445"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "[tensor([[[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]],\n",
      "\n",
      "\n",
      "        [[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]],\n",
      "\n",
      "\n",
      "        [[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]],\n",
      "\n",
      "\n",
      "        ...,\n",
      "\n",
      "\n",
      "        [[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]],\n",
      "\n",
      "\n",
      "        [[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]],\n",
      "\n",
      "\n",
      "        [[[0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          ...,\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.],\n",
      "          [0., 0., 0.,  ..., 0., 0., 0.]]]]), tensor([9, 9, 3, 3, 9, 0, 6, 1, 6, 7, 4, 8, 3, 7, 3, 3, 1, 0, 7, 4, 9, 7, 2, 3,\n",
      "        3, 5, 2, 6, 1, 5, 0, 5])]\n"
     ]
    }
   ],
   "source": [
    "train_loader = torch.utils.data.DataLoader(mnist_train,\n",
    "                                           batch_size=32, # batch size\n",
    "                                           shuffle=True)  # shuffle before each epoch\n",
    "\n",
    "for (xs, ts) in enumerate(train_loader):\n",
    "    print(xs) # image pixels\n",
    "    print(ts) # targets\n",
    "    break\n",
    "\n",
    "# Try changing the batch_size above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5JspElJK6wRY"
   },
   "source": [
    "## Putting it all together..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "yX2o12e46wRZ"
   },
   "outputs": [],
   "source": [
    "def run_gradient_descent(model,\n",
    "                         batch_size=64,\n",
    "                         learning_rate=0.01,\n",
    "                         weight_decay=0,\n",
    "                         num_epochs=10):\n",
    "    criterion = nn.CrossEntropyLoss()\n",
    "    optimizer = optim.SGD(model.parameters(), lr=learning_rate, weight_decay=weight_decay)\n",
    "\n",
    "    iters, losses = [], []\n",
    "    iters_sub, train_acc, val_acc  = [], [] ,[]\n",
    "\n",
    "    train_loader = torch.utils.data.DataLoader(\n",
    "        mnist_train,\n",
    "        batch_size=batch_size,\n",
    "        shuffle=True)\n",
    "\n",
    "    # training\n",
    "    n = 0 # the number of iterations\n",
    "    for epoch in range(num_epochs):\n",
    "        for xs, ts in iter(train_loader):\n",
    "            if len(ts) != batch_size:\n",
    "                continue\n",
    "            xs = xs.view(-1, 784)    # flatten the image. The -1 is a wildcard\n",
    "            zs = model(xs)\n",
    "            loss = criterion(zs, ts) # compute the total loss\n",
    "            loss.backward()          # compute updates for each parameter\n",
    "            optimizer.step()         # make the updates for each parameter\n",
    "            optimizer.zero_grad()    # a clean up step for PyTorch\n",
    "\n",
    "            # save the current training information\n",
    "            iters.append(n)\n",
    "            losses.append(float(loss)/batch_size)  # compute *average* loss\n",
    "\n",
    "            if n % 10 == 0:\n",
    "                iters_sub.append(n)\n",
    "                train_acc.append(get_accuracy(model, mnist_train))\n",
    "                val_acc.append(get_accuracy(model, mnist_val))\n",
    "            # increment the iteration number\n",
    "            n += 1\n",
    "\n",
    "    # plotting\n",
    "    plt.title(\"Training Curve (batch_size={}, lr={})\".format(batch_size, learning_rate))\n",
    "    plt.plot(iters, losses, label=\"Train\")\n",
    "    plt.xlabel(\"Iterations\")\n",
    "    plt.ylabel(\"Loss\")\n",
    "    plt.show()\n",
    "\n",
    "    plt.title(\"Training Curve (batch_size={}, lr={})\".format(batch_size, learning_rate))\n",
    "    plt.plot(iters_sub, train_acc, label=\"Train\")\n",
    "    plt.plot(iters_sub, val_acc, label=\"Validation\")\n",
    "    plt.xlabel(\"Iterations\")\n",
    "    plt.ylabel(\"Accuracy\")\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()\n",
    "\n",
    "    return model\n",
    "\n",
    "def get_accuracy(model, data):\n",
    "    loader = torch.utils.data.DataLoader(data, batch_size=500)\n",
    "\n",
    "    correct, total = 0, 0\n",
    "    for xs, ts in loader:\n",
    "        xs = xs.view(-1, 784) # flatten the image\n",
    "        zs = model(xs)\n",
    "        pred = zs.max(1, keepdim=True)[1] # get the index of the max logit\n",
    "        correct += pred.eq(ts.view_as(pred)).sum().item()\n",
    "        total += int(ts.shape[0])\n",
    "        return correct / total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Kl7PD23I6wRZ"
   },
   "source": [
    "Let's try training this model!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 590
    },
    "id": "0UIjtNDW6wRZ",
    "outputId": "23eefd75-928e-4aec-b7f8-d4f4f9b6af4c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Linear(in_features=784, out_features=10, bias=True)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = nn.Linear(784, 10)\n",
    "run_gradient_descent(model, batch_size=64, learning_rate=0.01, num_epochs=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "htW7WfSJ6wRZ"
   },
   "source": [
    "## Things to try:\n",
    "\n",
    "- Changing the batch size\n",
    "- Changing the weight decay parameter\n",
    "- Reduce the size of the training set (+ weight decay)\n",
    "- Changing the learning rate (for your project)"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "CS490_590_DL_Tutorial_2_Multiclass_Classification_with_PyTorch.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}